Question

prove it
$\frac{sin \: 2a}{1 - cos \: 2a } = cot \: a$

Answer 1

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$\bold{\underline{Question-}}$


prove it
$\frac{sin \: 2a}{1 - cos \: 2a } = cot \: a$



$\bold{\underline{Answer-}}$



LHS = $\frac{sin \: 2a}{1 - cos \: 2a }$

$= \frac{2sin \: a \: cos \: a}{1 - (1 - 2 {sin}^{2} a)}$

[°•°cos2A = 1 - 2sin² A]

$= \frac{2sin \: a \: cos \: a}{1 - 1 + 2 {sin}^{2}a } \\ \\ = \frac{2 \: sin \: a \: cos \: a}{2 {sin}^{2} a} \\ \\ \\ = \frac{cos \: a}{sin \: a} = cot \: a$